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Title: 3.1Discovery of the X Ray and the Electron


1
CHAPTER 3The Experimental Basis of Quantum Theory
  • 3.1 Discovery of the X Ray and the Electron
  • 3.2 Determination of Electron Charge
  • 3.3 Line Spectra
  • 3.4 Quantization
  • 3.5 Blackbody Radiation
  • 3.6 Photoelectric Effect
  • 3.7 X-Ray Production
  • 3.8 Compton Effect
  • 3.9 Pair Production and Annihilation

As far as I can see, our ideas are not in
contradiction to the properties of the
photoelectric effect observed by Mr. Lenard. -
Max Planck, 1905
2
3.1 Discovery of the X Ray and the Electron
  • X rays were discovered by Conrad Wilhelm Röntgen
    in 1895.
  • Observed x rays emitted by cathode rays
    bombarding glass.
  • Electrons were discovered by J. J. Thomson in
    1897.
  • Observed that cathode rays were charged
    particles.

3
Cathode Ray Experiments
  • In the 1890s scientists and engineers were
    familiar with cathode rays. These rays were
    generated from one of the metal plates in an
    evacuated tube across which a large electric
    potential had been established.
  • It was surmised that cathode rays had something
    to do with atoms.
  • It was known that cathode rays could penetrate
    matter and were deflected by magnetic and
    electric fields.

4
Observation of X Rays
  • Wilhelm Röntgen studied the effects of cathode
    rays passing through various materials. He
    noticed that a phosphorescent screen near the
    tube glowed during some of these experiments.
    These rays were unaffected by magnetic fields and
    penetrated materials more than cathode rays.
  • He called them x rays and deduced that they were
    produced by the cathode rays bombarding the glass
    walls of his vacuum tube.

5
Röntgens X Ray Tube
  • Röntgen constructed an x-ray tube by allowing
    cathode rays to impact the glass wall of the tube
    and produced x rays. He used x rays to image the
    bones of a hand on a phosphorescent screen.

6
Apparatus of Thomsons Cathode-Ray Experiment
  • Thomson used an evacuated cathode-ray tube to
    show that the cathode rays were negatively
    charged particles (electrons) by deflecting them
    in electric and magnetic fields.

7
Thomsons Experiment
  • Thomsons method of measuring the ratio of the
    electrons charge to mass was to send electrons
    through a region containing a magnetic field
    perpendicular to an electric field.

8
Calculation of e/m
  • An electron moving through the electric field is
    accelerated by a force
  • Electron angle of deflection
  • The magnetic field deflects the electron against
    the electric field force.
  • The magnetic field is adjusted until the net
    force is zero.
  • Charge to mass ratio

9
3.2 Determination of Electron Charge
  • Millikan oil drop experiment

10
Calculation of the oil drop charge
  • Used an electric field and gravity to suspend a
    charged oil drop.
  • Mass is determined from Stokess relationship of
    the terminal velocity to the radius and density.
  • Magnitude of the charge on the oil drop.
  • Thousands of experiments showed that there is a
    basic quantized electron charge.

C
11
3.3 Line Spectra
  • Chemical elements were observed to produce unique
    wavelengths of light when burned or excited in an
    electrical discharge.
  • Emitted light is passed through a diffraction
    grating with thousands of lines per ruling and
    diffracted according to its wavelength ? by the
    equation
  • where d is the distance of line separation and n
    is an integer called the order number.

12
Optical Spectrometer
  • Diffraction creates a line spectrum pattern of
    light bands and dark areas on the screen.
  • The line spectrum serves as a fingerprint of the
    gas that allows for unique identification of
    chemical elements and material composition.

13
Balmer Series
  • In 1885, Johann Balmer found an empirical formula
    for wavelength of the visible hydrogen line
    spectra in nm

nm (where k 3,4,5)
14
Rydberg Equation
  • As more scientists discovered emission lines at
    infrared and ultraviolet wavelengths, the Balmer
    series equation was extended to the Rydberg
    equation

15
3.4 Quantization
  • Current theories predict that charges are
    quantized in units (called quarks) of e/3 and
    2e/3, but quarks are not directly observed
    experimentally. The charges of particles that
    have been directly observed are quantized in
    units of e.
  • The measured atomic weights are not
    continuousthey have only discrete values, which
    are close to integral multiples of a unit mass.

16
3.5 Blackbody Radiation
  • When matter is heated, it emits radiation.
  • A blackbody is a cavity in a material that only
    emits thermal radiation. Incoming radiation is
    absorbed in the cavity.
  • Blackbody radiation is theoretically interesting
    because the radiation properties of the
    blackbody are independent of the particular
    material. Physicists can study the properties of
    intensity versus wavelength at fixed temperatures.

17
Wiens Displacement Law
  • The intensity (?, T) is the total power
    radiated per unit area per unit wavelength at a
    given temperature.
  • Wiens displacement law The maximum of the
    distribution shifts to smaller wavelengths as the
    temperature is increased.

18
Stefan-Boltzmann Law
  • The total power radiated increases with the
    temperature
  • This is known as the Stefan-Boltzmann law, with
    the constant s experimentally measured to be
    5.6705 10-8 W / (m2 K4).
  • The emissivity ? (? 1 for an idealized
    blackbody) is simply the ratio of the emissive
    power of an object to that of an ideal blackbody
    and is always less than 1.

19
Rayleigh-Jeans Formula
  • Lord Rayleigh (John Strutt) and James Jeans used
    the classical theories of electromagnetism and
    thermodynamics to show that the blackbody
    spectral distribution should be
  • It approaches the data at longer wavelengths, but
    it deviates badly at short wavelengths. This
    problem for small wavelengths became known as
    the ultraviolet catastrophe and was one of the
    outstanding exceptions that classical physics
    could not explain.

exp(x) 1 x for very small x, i.e. when h ? 0,
d. h. classical physics (also for f small and T
large)
20
Plancks Radiation Law
  • Planck assumed that the radiation in the cavity
    was emitted (and absorbed) by some sort of
    oscillators that were contained in the walls.
    He used Boltzmans statistical methods to arrive
    at the following formula that fit the blackbody
    radiation data.
  • Planck made two modifications to the classical
    theory
  • The oscillators (of electromagnetic origin) can
    only have certain discrete energies determined by
    En nhf, where n is an integer, f is the
    frequency, and h is called Plancks constant. h
    6.6261 10-34 Js.
  • The oscillators can absorb or emit energy in
    discrete multiples of the fundamental quantum of
    energy given by

Plancks radiation law
21
3.6 Photoelectric Effect
  • Methods of electron emission
  • Thermionic emission Application of heat allows
    electrons to gain enough energy to escape.
  • Secondary emission The electron gains enough
    energy by transfer from another high-speed
    particle that strikes the material from outside.
  • Field emission A strong external electric field
    pulls the electron out of the material.
  • Photoelectric effect Incident light
    (electromagnetic radiation) shining on the
    material transfers energy to the electrons,
    allowing them to escape.

Electromagnetic radiation interacts with
electrons within metals and gives the electrons
increased kinetic energy. Light can give
electrons enough extra kinetic energy to allow
them to escape. We call the ejected electrons
photoelectrons.
22
Experimental Setup
23
Experimental Results
  1. The kinetic energies of the photoelectrons are
    independent of the light intensity.
  2. The maximum kinetic energy of the photoelectrons,
    for a given emitting material, depends only on
    the frequency of the light.
  3. The smaller the work function f of the emitter
    material, the smaller is the threshold frequency
    of the light that can eject photoelectrons.
  4. When the photoelectrons are produced, however,
    their number is proportional to the intensity of
    light.
  5. The photoelectrons are emitted almost instantly
    following illumination of the photocathode,
    independent of the intensity of the light.

24
Experimental Results
25
Classical Interpretation
  • Classical theory predicts that the total amount
    of energy in a light wave increases as the light
    intensity increases.
  • The maximum kinetic energy of the photoelectrons
    depends on the value of the light frequency f and
    not on the intensity.
  • The existence of a threshold frequency is
    completely inexplicable in classical theory.
  • Classical theory would predict that for extremely
    low light intensities, a long time would elapse
    before any one electron could obtain sufficient
    energy to escape. We observe, however, that the
    photoelectrons are ejected almost immediately.

26
Einsteins Theory
  • Einstein suggested that the electromagnetic
    radiation field is quantized into particles
    called photons. Each photon has the energy
    quantum
  • where f is the frequency of the light and h is
    Plancks constant.
  • The photon travels at the speed of light in a
    vacuum, and its wavelength is given by

27
Einsteins Theory
  • Conservation of energy yields
  • where is the work function of the metal.
  • Explicitly the energy is
  • The retarding potentials measured in the
    photoelectric effect are the opposing potentials
    needed to stop the most energetic electrons.

28
Quantum Interpretation
  • The kinetic energy of the electron does not
    depend on the light intensity at all, but only on
    the light frequency and the work function of the
    material.
  • Einstein in 1905 predicted that the stopping
    potential was linearly proportional to the light
    frequency, with a slope h, the same constant
    found by Planck.
  • From this, Einstein concluded that light is a
    particle with energy

29
3.7 X-Ray Production
  • An energetic electron passing through matter will
    radiate photons and lose kinetic energy which is
    called bremsstrahlung, from the German word for
    braking radiation. Since linear momentum must
    be conserved, the nucleus absorbs very little
    energy, and it is ignored. The final energy of
    the electron is determined from the conservation
    of energy to be
  • An electron that loses a large amount of energy
    will produce an X-ray photon. Current passing
    through a filament produces copious numbers of
    electrons by thermionic emission. These electrons
    are focused by the cathode structure into a beam
    and are accelerated by potential differences of
    thousands of volts until they impinge on a metal
    anode surface, producing x rays by bremsstrahlung
    as they stop in the anode material.

30
Inverse Photoelectric Effect.
  • Conservation of energy requires that the electron
    kinetic energy equal the maximum photon energy
    where we neglect the work function because it is
    normally so small compared to the potential
    energy of the electron. This yields the
    Duane-Hunt limit which was first found
    experimentally. The photon wavelength depends
    only on the accelerating voltage and is the same
    for all targets.

31
3.8 Compton Effect
  • When a photon enters matter, it is likely to
    interact with one of the atomic electrons. The
    photon is scattered from only one electron,
    rather than from all the electrons in the
    material, and the laws of conservation of energy
    and momentum apply as in any elastic collision
    between two particles. The momentum of a particle
    moving at the speed of light is
  • The electron energy can be written as
  • This yields the change in wavelength of the
    scattered photon which is known as the Compton
    effect

32
3.9 Pair Production and Annihilation
  • If a photon can create an electron, it must also
    create a positive charge to balance charge
    conservation.
  • In 1932, C. D. Anderson observed a positively
    charged electron (e) in cosmic radiation. This
    particle, called a positron, had been predicted
    to exist several years earlier by P. A. M. Dirac.
  • A photons energy can be converted entirely into
    an electron and a positron in a process called
    pair production.

33
Pair Production in Empty Space
  • Conservation of energy for pair production in
    empty space is
  • Considering momentum conservation yields
  • This energy exchange has the maximum value
  • Recall that the total energy for a particle can
    be written as
  • However this yields a contradiction
  • and hence the conversion of energy in empty
    space is an impossible situation.

34
Pair Production in Matter
  • Since the relations
    and contradict each other, a
    photon can not produce an electron and a positron
    in empty space.
  • In the presence of matter, the nucleus absorbs
    some energy and momentum.
  • The photon energy required for pair production in
    the presence of matter is

35
Pair Annihilation
  • A positron passing through matter will likely
    annihilate with an electron. A positron is drawn
    to an electron by their mutual electric
    attraction, and the electron and positron then
    form an atomlike configuration called
    positronium.
  • Pair annihilation in empty space will produce two
    photons to conserve momentum. Annihilation near a
    nucleus can result in a single photon.
  • Conservation of energy
  • Conservation of momentum
  • The two photons will be almost identical, so that
  • The two photons from positronium annihilation
    will move in opposite directions with an energy
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